# Properties

 Label 7497.j Number of curves 2 Conductor 7497 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7497.j1")

sage: E.isogeny_class()

## Elliptic curves in class 7497.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7497.j1 7497f2 [0, 0, 1, -26166, -1630022] [] 13824
7497.j2 7497f1 [0, 0, 1, 294, -9347] [] 4608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7497.j have rank $$1$$.

## Modular form7497.2.a.j

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} + 3q^{11} + q^{13} + 4q^{16} - q^{17} + q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 